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51 Eri b is one of the only young planets consistent with a wide range ofpossible initial entropy states, including the cold-start scenario associatedwith some models of planet formation by core accretion. The most direct way toconstrain the initial entropy of a planet is by measuring its luminosity andmass at a sufficiently young age that the initial conditions still matter. Wepresent the tightest upper limit on 51 Eri b's mass yet (M < 11 Mjup at2$\sigma$) using a cross-calibration of Hipparcos and Gaia EDR3 astrometry andthe orbit-fitting code orvara. We also reassess its luminosity using a direct,photometric approach, finding log(Lbol/Lsun) = -5.5$\pm$0.2 dex. Combining thisluminosity with the 24$\pm$3 Myr age of the $\beta$ Pic moving group, of which51 Eri is a member, we derive mass distributions from a grid of evolutionarymodels that spans a wide range of initial entropies. We find that 51 Eri b isinconsistent with the coldest-start scenarios, requiring an initial entropy of>8 $k_B$/baryon at 97% confidence. This result represents the firstobservational constraint on the initial entropy of a potentially cold-startplanet, and it continues the trend of dynamical masses for directly imagedplanets pointing to warm- or hot-start formation scenarios.

Limits on the Mass and Initial Entropy of 51 Eri b from Gaia EDR3 Astrometry